Quantification of parametric uncertainty of ANN models with GLUE method for different streamflow dynamics

This study describes the parametric uncertainty of artificial neural networks (ANNs) by employing the generalized likelihood uncertainty estimation (GLUE) method. The ANNs are used to forecast daily streamflow for three sub-basins of the Rhine Basin (East Alpine, Main, and Mosel) having different hydrological and climatological characteristics. We have obtained prior parameter distributions from 5000 ANNs in the training period to capture the parametric uncertainty and subsequently 125,000 correlated parameter sets were generated. These parameter sets were used to quantify the uncertainty in the forecasted streamflow in the testing period using three uncertainty measures: percentage of coverage, average relative length, and average asymmetry degree. The results indicated that the highest uncertainty was obtained for the Mosel sub-basin and the lowest for the East Alpine sub-basin mainly due to hydro-climatic differences between these basins. The prediction results and uncertainty estimates of the proposed methodology were compared to the direct ensemble and bootstrap methods. The GLUE method successfully captured the observed discharges with the generated prediction intervals, especially the peak flows. It was also illustrated that uncertainty bands are sensitive to the selection of the threshold value for the Nash–Sutcliffe efficiency measure used in the GLUE method by employing the Wilcoxon–Mann–Whitney test.     

Seasonal copula models for the analysis of glacier discharge at King George Island,Antarctica

Modelling glacier discharge is an important issue in hydrology and climate research. Glaciers represent a fundamental water resource when melting of ice and snow contributes to runoff. Glaciers are also studied as natural global warming sensors. GLACKMA association has implemented one of their Pilot Experimental Catchment areas at the King George Island in the Antarctica which records values of the liquid discharge from Collins glacier. In this paper, we propose the use of time-varying copula models for analyzing the relationship between air temperature and glacier discharge, which is clearly non constant and non linear through time. A seasonal copula model is defined where both the marginal and copula parameters vary periodically along time following a seasonal dynamic. Full Bayesian inference is performed such that the marginal and copula parameters are estimated in a one single step, in contrast with the usual two-step approach. Bayesian prediction and model selection is also carried out for the proposed model such that Bayesian credible intervals can be obtained for the conditional glacier discharge given a value of the temperature at any given time point. The proposed methodology is illustrated using the GLACKMA real data where there is, in addition, a hydrological year of missing discharge data which were not possible to measure accurately due to problems in the sounding.     

On the criteria of model performance evaluation for real-time flood forecasting

Model performance evaluation for real-time flood forecasting has been conducted using various criteria. Although the coefficient of efficiency (ss="EmphasisTypeItalic ">CE) is most widely used, we demonstrate that a model achieving good model efficiency may actually be inferior to the naïve (or persistence) forecasting, if the flow series has a high lag-1 autocorrelation coefficient. We derived sample-dependent and AR model-dependent asymptotic relationships between the coefficient of efficiency and the coefficient of persistence (ss="EmphasisTypeItalic ">CP) which form the basis of a proposed ss="EmphasisTypeItalic ">CE–ss="EmphasisTypeItalic ">CP coupled model performance evaluation criterion. Considering the flow persistence and the model simplicity, the AR(2) model is suggested to be the benchmark model for performance evaluation of real-time flood forecasting models. We emphasize that performance evaluation of flood forecasting models using the proposed ss="EmphasisTypeItalic ">CE–ss="EmphasisTypeItalic ">CP coupled criterion should be carried out with respect to individual flood events. A single ss="EmphasisTypeItalic ">CE or ss="EmphasisTypeItalic ">CP value derived from a multi-event artifactual series by no means provides a multi-event overall evaluation and may actually disguise the real capability of the proposed model.     

Short‐ and long‐term evapotranspiration rates at ecological restoration sites along a large river receiving rare flow events

Many large rivers around the world no longer flow to their deltas, due to ever greater water withdrawals and diversions for human needs. However, the importance of riparian ecosystems is drawing increasing recognition, leading to the allocation of environmental flows to restore river processes. Accurate estimates of riparian plant evapotranspiration (ET) are needed to understand how the riverine system responds to these rare events and achieve the goals of environmental flows. In 2014, historic environmental flows were released into the Lower Colorado River at Morelos Dam (Mexico); this once perennial but now dry reach is the final stretch to the mighty Colorado River Delta. One of the primary goals was to supply native vegetation restoration sites along the reach with water to help seedlings establish and boost groundwater levels to foster the planted saplings. Patterns in ET before, during, and after the flows are useful for evaluating whether this goal was met and understanding the role that ET plays in this now ephemeral river system. Here, diurnal fluctuations in groundwater levels and Moderate Resolution Imaging Spectroradiometer (MODIS) data were used to compare estimates of ET specifically at 3 native vegetation restoration sites during 2014 planned flow events, and MODIS data were used to evaluate long‐term (2002–2016) ET responses to restoration efforts at these sites. Overall, ET was generally 0–10&nbsp;mm d<sup>?1sup> across sites, and although daily ET values from groundwater data were highly variable, weekly averaged estimates were highly correlated with MODIS‐derived estimates at most sites. The influence of the 2014 flow events was not immediately apparent in the results, although the process of clearing vegetation and planting native vegetation at the restoration sites was clearly visible in the results.     

Perched lobe formation in the Gulf of Cadiz: Interactions between gravity processes and contour currents (Algarve Margin, Southern Portugal)

The Gulf of Cadiz is swept by the strong saline Mediterranean Outflow Water (MOW). On the Algarve Margin (South Portugal), this current has constructed fine-grained contourite drifts. This margin is dissected by the Portimao Canyon and three short channels that only incise the upper slope, and are absent on a terrace located at mid-slope depths along the Algarve Margin. High-resolution seismic profiles and sediment cores highlight the original architecture of the sedimentary deposits on this terrace. Coarse-grained lenticular chaotic bodies formed during major relative sea-level lowstands are intercalated within the drift. The lobate shape and sandy nature of the lenticular chaotic bodies and their location at the mouths of the three short channels suggest they are gravity-generated deposits that are perched on the middle continental slope.In the Gulf of Cadiz, the interaction between contour current and gravity processes is strongly controlled by climatic variations and relative sea-level changes during the late Quaternary. During cold periods when sea-level was low, erosion intensified on the continental shelf and the deepest part of MOW was active. Sediment was transported downslope through the channels and deposited on sedimentary lobes perched on the mid-slope terrace. During warm periods when relative sea-level was high, the supply of sediment from the shelf was shut off and the shallowest part of MOW was more active. Contourite drifts fill the channels and bury the sandy lobes.     

An experimental study of Fe–Ni exchange between sulfide melt and olivine at upper mantle conditions: implications for mantle sulfide compositions and phase equilibria

The behavior of nickel in the Earth’s mantle is controlled by sulfide melt–olivine reaction. Prior to this study, experiments were carried out at low pressures with narrow range of Ni/Fe in sulfide melt. As the mantle becomes more reduced with depth, experiments at comparable conditions provide an assessment of the effect of pressure at low-oxygen fugacity conditions. In this study, we constrain the Fe–Ni composition of molten sulfide in the Earth’s upper mantle via sulfide melt–olivine reaction experiments at 2 GPa, 1200 and 1400 °C, with sulfide melt <span class="InlineEquation" id="IEq1">\(X_{{{\text{Ni}}}}^{{{\text{Sulfide}}}}=\frac{{{\text{Ni}}}}{{{\text{Ni}}+{\text{Fe}}}}\)span> (atomic ratio) ranging from 0 to 0.94. To verify the approach to equilibrium and to explore the effect of <span class="InlineEquation" id="IEq2">\({f_{{{\text{O}}_{\text{2}}}}}\)span> on Fe–Ni exchange between phases, four different suites of experiments were conducted, varying in their experimental geometry and initial composition. Effects of Ni secondary fluorescence on olivine analyses were corrected using the PENELOPE algorithm (Baró et al., Nucl Instrum Methods Phys Res B 100:31–46, 1995), “zero time” experiments, and measurements before and after dissolution of surrounding sulfides. Oxygen fugacities in the experiments, estimated from the measured O contents of sulfide melts and from the compositions of coexisting olivines, were 3.0?±?1.0 log units more reduced than the fayalite–magnetite-quartz (FMQ) buffer (suite 1, 2 and 3), and FMQ ??1 or more oxidized (suite 4). For the reduced (suites 1–3) experiments, Fe–Ni distribution coefficients <span class="InlineEquation" id="IEq3">\(K_{{\text{D}}}^{{}}=\frac{{(X_{{{\text{Ni}}}}^{{{\text{sulfide}}}}/X_{{{\text{Fe}}}}^{{{\text{sulfide}}}})}}{{(X_{{{\text{Ni}}}}^{{{\text{olivine}}}}/X_{{{\text{Fe}}}}^{{{\text{olivine}}}})}}\)span> are small, averaging 10.0?±?5.7, with little variation as a function of total Ni content. More oxidized experiments (suite 4) give larger values of ss="EmphasisTypeItalic ">K<sub>Dsub> (21.1–25.2). Compared to previous determinations at 100 kPa, values of ss="EmphasisTypeItalic ">K<sub>Dsub> from this study are chiefly lower, in large part owing to the more reduced conditions of the experiments. The observed difference does not seem attributable to differences in temperature and pressure between experimental studies. It may be related in part to the effects of metal/sulfur ratio in sulfide melt. Application of these results to the composition of molten sulfide in peridotite indicates that compositions are intermediate in composition (<span class="InlineEquation" id="IEq4">\(X_{{{\text{Ni}}}}^{{{\text{sulfide}}}}\)span>?~?0.4–0.6) in the shallow mantle at 50 km, becomes more Ni rich with depth as the O content of the melt diminishes, reaching a maximum (0.6–0.7) at depths near 80–120 km, and then becomes more Fe rich in the deeper mantle where conditions are more reduced, approaching (<span class="InlineEquation" id="IEq5">\(X_{{{\text{Ni}}}}^{{{\text{sulfide}}}}\)span>?~?0.28)?>?140 km depth. Because Ni-rich sulfide in the shallow upper mantle melts at lower temperature than more Fe-rich compositions, mantle sulfide is likely molten in much of the deep continental lithosphere, including regions of diamond formation.     

Experimental calibration of Forsterite–Anorthite–Ca-Tschermak–Enstatite (FACE) geobarometer for mantle peridotites

ss="Para">The crystallization of plagioclase-bearing assemblages in mantle rocks is witness of mantle exhumation at shallow depth. Previous experimental works on peridotites have found systematic compositional variations in coexisting minerals at decreasing pressure within the plagioclase stability field. In this experimental study we present new constraints on the stability of plagioclase as a function of different Na<sub>2sub>O/CaO bulk ratios, and we present a new geobarometer for mantle rocks. Experiments have been performed in a single-stage piston cylinder at 5–10 kbar, 1050–1150?°C at nominally anhydrous conditions using seeded gels of peridotite compositions (Na<sub>2sub>O/CaO?=?0.08–0.13; ss="EmphasisTypeItalic ">X <sub>Crsub> = Cr/(Cr?+?Al)?=?0.07–0.10) as starting materials. As expected, the increase of the bulk Na<sub>2sub>O/CaO ratio extends the plagioclase stability to higher pressure; in the studied high-Na fertile lherzolite (HNa-FLZ), the plagioclase-spinel transition occurs at 1100?°C between 9 and 10 kbar; in a fertile lherzolite (FLZ) with Na<sub>2sub>O/CaO?=?0.08, it occurs between 8 and 9 kbar at 1100?°C. This study provides, together with previous experimental results, a consistent database, covering a wide range of ss="EmphasisTypeItalic ">P–ss="EmphasisTypeItalic ">T conditions (3–9 kbar, 1000–1150?°C) and variable bulk compositions to be used to define and calibrate a geobarometer for plagioclase-bearing mantle rocks. The pressure sensitive equilibrium:

ss="Equation EquationMathjax">

ss="EquationContent">$$\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{4}}}^{{\text{Ol}}}}\limits_{{\text{Forsterite}}} +\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{8}}}^{{\text{Pl}}}}\limits_{{\text{Anorthite}}~} =\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{6}}}^{{\text{Cpx}}}}\limits_{{\text{Ca-Tschermak}}} +{\text{ }}\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{6}}}^{{\text{Opx}}}}\limits_{{\text{Enstatite}}} ,$$

has been empirically calibrated by least squares regression analysis of experimental data combined with Monte Carlo simulation. The result of the fit gives the following equation:

ss="Equation EquationMathjax">

ss="EquationContent">$$P=7.2( \pm 2.9)+0.0078( \pm 0.0021)T{\text{ }}+0.0022( \pm 0.0001)T{\text{ }}\ln K,$$

ss="Equation EquationMathjax">

ss="EquationContent">$${R^2}=0.93,$$

where ss="EmphasisTypeItalic ">P is expressed in kbar andss="EmphasisTypeItalic "> T in kelvin. ss="EmphasisTypeItalic ">K is the equilibrium constant ss="EmphasisTypeItalic ">K?=?ss="EmphasisTypeItalic ">a <sub>CaTssub> × ss="EmphasisTypeItalic ">a <sub>ensub>/ss="EmphasisTypeItalic ">a <sub>ansub> × ss="EmphasisTypeItalic ">a <sub>fosub>, where ss="EmphasisTypeItalic ">a <sub>CaTssub>, ss="EmphasisTypeItalic ">a <sub>ensub>, ss="EmphasisTypeItalic ">a <sub>ansub> and ss="EmphasisTypeItalic ">a <sub>fosub> are the activities of Ca-Tschermak in clinopyroxene, enstatite in orthopyroxene, anorthite in plagioclase and forsterite in olivine. The proposed geobarometer for plagioclase peridotites, coupled to detailed microstructural and mineral chemistry investigations, represents a valuable tool to track the exhumation of the lithospheric mantle at extensional environments.

     

Tracing the flow of organic matter from primary producers to filter feeders in Ria Formosa lagoon, Southern Portugal

The flow of organic matter along the main navigation channel of Ria Formosa, Portugal, was assessed using determinations of suspended particulate matter (SPM), particulate organic matter (POM), and chlorophyll a (chla) concentrations in conjunction with stable isotope values of primary producers, particulate matter, and two filter feeders. SPM in the lagoon is dominated by inorganic particles comprising 80% of total weight with organic matter averaging about 20%. The algal component of the POM averaged about 5% with the remainder comprised of detritus. The δ<sup>13sup>C values of primary producers ranged from ?9.1‰ in the intertidal seagrassZostera noltii to ?30.7‰ in the red seaweedBostrychia scorpioides revealing underlying differences in the mechanisms of carbon uptake. The δ<sup>13sup>C value ofB. scorpioides, which develops entangled on the salt marsh speciesSpartina maritima, suggests that its main source of inorganic carbon is atmospheric CO<sub>2sub>. The δ<sup>13sup>C values of the high marsh macrophyteSarcocornia perennis significantly increased with distance from the ocean while δ<sup>13sup>C values ofZ. noltii decreased, probably because higher decomposition of organic matter at inner stations lowers the δ<sup>13sup>CO<sub>2sub> value in the water. The δ<sup>15sup>N values of Ulvales, seagrasses, and marsh plants significantly increased from outer stations to inner stations. This increase may be due either to recycling of nitrogen (N) within the marsh (with loss of light N<sub>2sub> or NH<sub>4sub>) or to inputs of isotopically heavy N from sewage. The δ<sup>15sup>N values of particulate matter showed an opposite trend, which indicates higher microbial degradation of organic matter at the inner lagoon. The data demonstrate that the seston in the lagoon is a mixture of detritus from lagoon primary producers with a minor contribution of microalgae. The filter feeders are most likely assimilating a mixture of phytoplankton and microphytobenthos. Digestion of lagoon seston is selective. The δ<sup>15sup>N values of both muscle and digestive gland of filter feeders showed the opposite gradient of particulate matter indicating that the depleted δ<sup>15sup>N of SPM at inner stations was not assimilated or even ingested. Stable isotopes values did not differ between the filter-feeders—the musselMytilus galloprovincialis collected on buoys and the clamTapes decussatus collected in the sediment—suggesting a considerable mixture of benthic-pelagic organic matter throughout the water column. Assessment of the changes in isotopic decomposition of detritus as it decays is required to refine our understanding of organic matter transfers in detrital food webs.